Solve sqrt{(17-8)}:sqrt{(5,4+1,6)}*2-5

$$\sqrt { ( 17 - 8 ) } : \sqrt { ( 5,4 + 1,6 ) } \cdot 2 - 5$$

Evaluate

$$\frac{6\sqrt{7}}{7}-5\approx -2.732213162$$

Short Solution Steps

Subtract 8 from 17 to get 9.

$$2\times \frac{\sqrt{9}}{\sqrt{5,4+1,6}}-5$$

Calculate the square root of 9 and get 3.

$$2\times \frac{3}{\sqrt{5,4+1,6}}-5$$

Add 5,4 and 1,6 to get 7.

$$2\times \frac{3}{\sqrt{7}}-5$$

Rationalize the denominator of \frac{3}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$2\times \frac{3\sqrt{7}}{\left(\sqrt{7}\right)^{2}}-5$$

The square of \sqrt{7} is 7.

$$2\times \frac{3\sqrt{7}}{7}-5$$

Express 2\times \frac{3\sqrt{7}}{7} as a single fraction.

$$\frac{2\times 3\sqrt{7}}{7}-5$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{7}{7}.

$$\frac{2\times 3\sqrt{7}}{7}-\frac{5\times 7}{7}$$

Since \frac{2\times 3\sqrt{7}}{7} and \frac{5\times 7}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 3\sqrt{7}-5\times 7}{7}$$

Do the multiplications in 2\times 3\sqrt{7}-5\times 7.

$$\frac{6\sqrt{7}-35}{7}$$